Enabling Controlling Complex Networks with Local Topological Information

Prevalence and scalable control of localized networks

The ability to control network dynamics is essential for ensuring desirable functionality of many technological, biological, and social systems. Such systems often consist of a large number of network elements, and controlling large-scale networks remains challenging because the computation and communication requirements increase prohibitively fast with network size. Here, we introduce a notion of network locality that can be exploited to make the control of networks scalable, even when the dynamics are nonlinear. We show that network locality is captured by an information metric and is almost universally observed across real and model networks. In localized networks, the optimal control actions and system responses are both shown to be necessarily concentrated in small neighborhoods induced by the information metric. This allows us to develop localized algorithms for determining network controllability and optimizing the placement of driver nodes. This also allows us to develop a localized algorithm for designing local feedback controllers that approach the performance of the corresponding best global controllers, while incurring a computational cost orders-of-magnitude lower. We validate the locality, performance, and efficiency of the algorithms in Kuramoto oscillator networks, as well as three large empirical networks: synchronization dynamics in the Eastern US power grid, epidemic spreading mediated by the global air-transportation network, and Alzheimer's disease dynamics in a human brain network. Taken together, our results establish that large networks can be controlled with computation and communication costs comparable to those for small networks.

Modeling and Optimization of a Molecular Biocontroller for the Regulation of Complex Metabolic Pathways

Achieving optimal production in microbial cell factories, robustness against changing intracellular and environmental perturbations requires the dynamic feedback regulation of the pathway of interest. Here, we consider a merging metabolic pathway motif, which appears in a wide range of metabolic engineering applications, including the production of phenylpropanoids among others. We present an approach to use a realistic model that accounts for in vivo implementation and then propose a methodology based on multiobjective optimization for the optimal tuning of the gene circuit parts composing the biomolecular controller and biosensor devices for a dynamic regulation strategy. We show how this approach can deal with the trade-offs between the performance of the regulated pathway, robustness to perturbations, and stability of the feedback loop. Using realistic models, our results suggest that the strategies for fine-tuning the trade-offs among performance, robustness, and stability in dynamic pathway regulation are complex. It is not always possible to infer them by simple inspection. This renders the use of the multiobjective optimization methodology valuable and necessary.

Energy cost study for controlling complex social networks with conformity behavior

To understand controlling a complex system, an estimation of the required effort needed to achieve control is vital. Previous works have addressed this issue by studying the scaling laws of energy cost in a general way with continuous-time linear dynamics. However, continuous-time linear dynamics is unable to capture conformity behavior, which is common in many complex social systems. Therefore, to understand controlling social systems with conformity, discrete-time modeling is used and the energy cost scaling laws are derived. The results are validated numerically with model and real networks. In addition, the energy costs needed for controlling systems with and without conformity are compared, and it was found that controlling networked systems with conformity features always requires less control energy. Finally, it is shown through simulations that heterogeneous scale-free networks are less controllable, requiring a higher number of minimum drivers. Since the conformity-based model relates to various complex systems, such as flocking, or evolutionary games, the results of this paper represent a step forward toward developing realistic control of complex social systems.

A Link Prediction Method Based on Neural Networks

Link prediction to optimize network performance is of great significance in network evolution. Because of the complexity of network systems and the uncertainty of network evolution, it faces many challenges. This paper proposes a new link prediction method based on neural networks trained on scale-free networks as input data, and optimized networks trained by link prediction models as output data. In order to solve the influence of the generalization of the neural network on the experiments, a greedy link pruning strategy is applied. We consider network efficiency and the proposed global network structure reliability as objectives to comprehensively evaluate link prediction performance and the advantages of the neural network method. The experimental results demonstrate that the neural network method generates the optimized networks with better network efficiency and global network structure reliability than the traditional link prediction models.

Optimizing target nodes selection for the control energy of directed complex networks

The energy needed in controlling a complex network is a problem of practical importance. Recent works have focused on the reduction of control energy either via strategic placement of driver nodes, or by decreasing the cardinality of nodes to be controlled. However, optimizing control energy with respect to target nodes selection has yet been considered. In this work, we propose an iterative method based on Stiefel manifold optimization of selectable target node matrix to reduce control energy. We derive the matrix derivative gradient needed for the search algorithm in a general way, and search for target nodes which result in reduced control energy, assuming that driver nodes placement is fixed. Our findings reveal that the control energy is optimal when the path distances from driver nodes to target nodes are minimized. We corroborate our algorithm with extensive simulations on elementary network topologies, random and scale-free networks, as well as various real networks. The simulation results show that the control energy found using our algorithm outperforms heuristic selection strategies for choosing target nodes by a few orders of magnitude. Our work may be applicable to opinion networks, where one is interested in identifying the optimal group of individuals that the driver nodes can influence.

Multi-Agent Systems and Complex Networks: Review and Applications in Systems Engineering

Systems engineering is an ubiquitous discipline of Engineering overlapping industrial, chemical, mechanical, manufacturing, control, software, electrical, and civil engineering. It provides tools for dealing with the complexity and dynamics related to the optimisation of physical, natural, and virtual systems management. This paper presents a review of how multi-agent systems and complex networks theory are brought together to address systems engineering and management problems. The review also encompasses current and future research directions both for theoretical fundamentals and applications in the industry. This is made by considering trends such as mesoscale, multiscale, and multilayer networks along with the state-of-art analysis on network dynamics and intelligent networks. Critical and smart infrastructure, manufacturing processes, and supply chain networks are instances of research topics for which this literature review is highly relevant.

Minimum Cost Control of Directed Networks With Selectable Control Inputs

The minimum cost control problem is one of the most important issues in controlling complex networks. Different from the previous works, in this paper, we consider the minimum cost control problem with selectable inputs by adopting the cost function summed over both quadratic terms of system input and system state with a weighting factor. To address such an issue, the orthonormal-constraint-based projected gradient method is proposed to determine the input matrix iteratively. Convergence of the proposed algorithm is established. Extensive simulation results are carried out to show the effectiveness of the proposed algorithm. We also investigate what kinds of nodes are most important for minimizing average control cost in directed stems/circles and small networks through simulation studies. The presented results in this paper bring meaningful physical insights in controlling the directed networks from an energy point of view.

Topology Effects on Sparse Control of Complex Networks with Laplacian Dynamics

Ease of control of complex networks has been assessed extensively in terms of structural controllability and observability, and minimum control energy criteria. Here we adopt a sparsity-promoting feedback control framework for undirected networks with Laplacian dynamics and distinct topological features. The control objective considered is to minimize the effect of disturbance signals, magnitude of control signals and cost of feedback channels. We show that depending on the cost of feedback channels, different complex network structures become the least expensive option to control. Specifically, increased cost of feedback channels favors organized topological complexity such as modularity and centralization. Thus, although sparse and heterogeneous undirected networks may require larger numbers of actuators and sensors for structural controllability, networks with Laplacian dynamics are shown to be easier to control when accounting for the cost of feedback channels.

Matrix function optimization under weighted boundary constraints and its applications in network control

The matrix function optimization under weighted boundary constraints on the matrix variables is investigated in this work. An "index-notation-arrangement based chain rule" (I-Chain rule) is introduced to obtain the gradient of a matrix function. By doing this, we propose the weighted trace-constraint-based projected gradient method (WTPGM) and weighted orthornormal-constraint-based projected gradient method (WOPGM) to locate a point of minimum of an objective/cost function of matrix variables iteratively subject to weighted trace constraint and weighted orthonormal constraint, respectively. New techniques are implemented to establish the convergence property of both algorithms. In addition, compared with the existing scheme termed "orthornormal-constraint-based projected gradient method" (OPGM) that requires the gradient has to be represented by the multiplication of a symmetrical matrix and the matrix variable itself, such a condition has been relaxed in WOPGM. Simulation results show the effectiveness of our methods not only in network control but also in other learning problems. We believe that the results reveal interesting physical insights in the field of network control and allow extensive applications of matrix function optimization problems in science and engineering.